I'm sorry, there are thousands of valid ways to enjoy our hobby, and as "just a game" is a completely valid one. There's even a well known description of a "beer and pretzels" game showing there's a whole category of people who enjoy it so, and that's just very casual "just a game" games, not inclusive of all of the people who play it as "just a game".
It is not correct to assume it will always include other aspects like you are putting forth.
All the other aspects that I'm putting forth are inherently part of games. Especially a game like D&D. Once again, to clear things up, I am
not talking about learning concrete knowledge like learning to do math, or learn empathy (even though TTRPGs are also inherently good for that). I am also
not talking about one person teaching someone else something.
I'm talking about the simple loop where you acquire new knowledge, new experiences while playing a game, you learn from it and you adjust the way you play. You use your
Witch Bolt on an enemy that's quite fragile and it dies too soon, you realize that it's best used on enemies that are tougher. You fight a tough enemy, and one of your player dies, you realize that you didn't have all the information you needed to face it.
I introduced my niece (9 years old) to D&D three weeks go, and there's a ton of it. Just learning the core mechanics of the game changed her behaviour drastically within half an hour. Understanding that asking for riskier things will lead to a check which success chances depends on a number on her sheet made her change the way she played.
It can be knowledge outside the game: like understanding the rules, learning what type of players you're sitting with, what kind of DM you're playing with, etc. It can be knowledge in the game: how your abilities are best used, what happens when you make a certain choice, how ward a certain task is, what faction an NPC is part of. Players just learn things and they change the way they play. Even in a beer and pretzel game. That's just what humans do.
To bring things back on topic, and to what my initial point was. I think that fudging is in most cases bad for player agency, and that if it's something you do frequently and your players understand it unconciously, it will affect their behavior at the table. They might become careless, disinterested, frustrated; it depends on them and your type of play. But I fail to see what good reactions could come out of a player realizing the impact of his choices are being diluted.